Fin for a finned pack for heat exchangers as well as a heat exchanger

ABSTRACT

The present invention regards a fin for a finned pack for heat exchangers, including a plate in which a plurality of through holes is formed for the positioning of tubes intended to convey a first heat exchange fluid, the plate having an edge as well as two main faces, each intended to be licked by a second heat exchange fluid in a crossing direction (A-A) from an inlet portion to an outlet portion of the edge of the plate.

TECHNICAL FIELD OF THE INVENTION

The present invention regards a fin for a finned pack for heatexchangers, a finned pack and a heat exchanger including the latter.

DESCRIPTION OF RELATED ART

Heat exchangers are used in many applications for heating or cooling afirst fluid by placing it in heat exchange communication with a secondfluid. This is usually obtained by conveying a first fluid in tubeswhich cross passage zones of the second fluid.

Different types of heat exchangers have been proposed, including theso-called “finned pack” heat exchangers, which comprise a plurality ofpacked fins. Such fins comprise plate-like elements having a pluralityof holes in which tubes for conveying a first fluid are inserted, whilea second fluid is sent between the fins for the heat exchange with thefirst fluid.

The fins can have substantially smooth or corrugated geometry, i.e. inparticular if it is desired to increase the surface area or theefficiency of the heat exchange.

Nevertheless, the efficiency of the heat exchange in the exchangersaccording to the state of the art is often limited and there istherefore the need to improve the performances obtainable in heatexchangers.

US2004/194936A1, WO2014/104576A1, WO2011/082922A1, EP2072939A1 andCN102135388A1 teach solutions according to the state of the art.

SUMMARY OF THE INVENTION

One object of the present invention is to provide a new fin of a finnedpack for heat exchangers as well as a new finned pack and a new heatexchanger obtainable starting from one such fin.

Another object of the present invention is to provide a new fin of afinned pack that is able to ensure a greater heat exchange efficiency.

Another object of the present invention is to provide a fin like theaforesaid which allows affecting the external surface of the tubes ofthe exchanger in a uniform manner.

In accordance with one aspect of the invention, a fin is providedaccording to the present application.

The present application refers to preferred and advantageous embodimentsof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics and advantages of the invention will be moreevident from the description of embodiments of fins, of a finned packand of heat exchangers, illustrated as an example in the encloseddrawings in which:

FIG. 1 is a plan view of a fin according to the present invention;

FIG. 2 is a view of an enlarged-scale detail of the fin of FIG. 1 withtubes inserted;

FIG. 3 is a view of a detail of FIG. 2 with indications regardingseveral angles and distances;

FIG. 4 is a sectional view of a detail of a finned pack according to thepresent invention;

FIG. 5 is a view similar to FIG. 2 of another embodiment of a fin inaccordance with the present invention;

FIG. 6 is a slightly top perspective view that illustrates severalcomponents of a finned pack with fins according to FIG. 5;

FIG. 7 is a view of a finned pack according to the present invention andincluding a fin in accordance with the present invention; and

FIGS. 8 to 10 are views of heat exchangers in which a finned pack isinstallable according to the present invention.

In the set of drawings, equivalent parts or components are marked withthe same reference numbers.

DETAILED DESCRIPTION OF THE INVENTION

With reference to FIGS. 1 to 4, a fin 1 is illustrated for a finned packfor heat exchangers, which comprises a plate 2 in which a plurality ofthrough holes 3 is obtained for the positioning of tubes 4 intended toconvey a first heat exchange fluid, e.g. a liquid.

The plate 2 has an edge 5 as well as two main faces 6, each intended tobe licked or hit by a second heat exchange fluid, such as air, in acrossing direction A-A from an inlet portion 5 a to an outlet portion 5b of the edge 5 of the plate 2. For such purpose, the facing main faces6 of two adjacent and successive fins 1 together delimit a respectivearea of passage or crossing of a second fluid, which hits respectivesections of tubes 4 inserted in such fins.

The edge 5 actually constitutes a face of external connection betweenthe two main faces 6 and the same can be provided with two main sides 5a, 5 b, e.g. parallel, which are bridge connected by means of secondaryor smaller sides 5 c, 5 d, also if desired parallel and orthogonal tothe main sides. The main sides 5 a, 5 b actually constitute,respectively, the inlet portion 5 a and the outlet portion 5 b.

The holes 3 are delimited by a respective inner delimiting wall 7 of theplate 2, which includes a first portion 7 a facing towards the inletportion 5 a and a second portion 7 b (equal to or greater than theportion 7 a) facing towards the outlet portion 5 b. The delimiting wall7 for the holes 3 can be substantially cylindrical.

The fin 1 then comprises one or more confinement units 8, 9 for the flowof the second fluid, each confinement unit being placed around arespective section of the second portion 7 b of the delimiting wall 7 ofa hole 3 of the plurality of holes so as to obtain or define a partiallysurrounded hole or better yet a respective partially surrounded hole 3.Preferably, a confinement unit 8, 9 is provided for each hole 3 of thefin 1 or in any case for most of the holes 3 of the fin itself.

More particularly, at least one confinement unit comprises two firstbaffles 8, 9 or two through recesses for housing second baffles placedon opposite sides from each other with respect to a respective partiallysurrounded hole 3, and each enclosing and spaced by a respective sectionof the second portion 7 b of the delimiting wall 7 of the partiallysurrounded hole 3, so as to confine on the plate 2, during use, a firstflow zone FZ1 of the second fluid between each baffle 8, 9 or recess anda respective section of the second portion 7 b of the delimiting wall 7.

The configuration that will be described with reference to the firstbaffles is also applied in substance to the second baffles and viceversa, if it is considered that, once a finned pack is assembled, suchcomponents (first or second baffles) are intended to carry out the sametask and substantially in the same manner.

The first flow zone FZ1 comprises a mouth for introducing the secondfluid delimited between the plate 2, the first baffles 8, 9 and a partof the delimiting wall 7 as well as a mouth for delivering the secondfluid leading into an area downstream of the respective hole 3, i.e. anarea after the hole 3 in the sense of the crossing direction A-A. Thefirst flow zone FZ1 or better yet the walls thereof are fluid-sealed soas to prevent leaks or outflows of liquid between the introduction mouthand the delivery mouth.

With regard to the introduction mouth, it is preferably delimitedbetween the plate 2, a first end 8 a, 9 a of the first baffles 8, 9 orrecesses and a part of the second portion 7 b of the delimiting wall 7.

In addition, the distance of each baffle 8, 9 or of the recessesrelative to a respective partially surrounded hole 3, with reference tothe sense moving away from the inlet portion 5 a and approaching theoutlet portion 5 b, has one of the following geometries or extensions:

it is constant for the entire extension of the baffle or recess 8, 9,

it is constant and then increases,

it decreases for the entire extension of the baffle or recess 8, 9,

it decreases and then increases,

it is constant and then decreases, or

it is constant, then decreases and finally increases.

Such distance is calculated on a plane orthogonal to the axis x-x of apartially surrounded hole 3 and along an axis that connects the centeror central point of the partially surrounded hole 3 with the baffle 8, 9or better yet with the intrados of the baffle 8, 9 or of the recesses,i.e. the section of the baffles 8, 9 or recesses directed towards orfacing the respective partially surrounded hole 3.

More particularly, the first flow zone FZ1 has a section, evaluated withreference to a plane orthogonal to the plate 2 or in any case to themain extension plane thereof, and passing through the center or acentral point of the respective partially surrounded hole 3, that is:

constant for the entire extension thereof,

constant and then diverging,

converging for the entire extension thereof,

converging and then diverging,

constant and then converging, or

constant, then converging and finally diverging.

In substance, the first flow zone FZ1 does not have stagnation areas,i.e. it does not have first areas with section, evaluated with referenceto a plane orthogonal to the plate 2 and passing through the center or acentral point of the respective partially surrounded hole 3, greaterthan areas downstream and upstream, with reference to the sense from theinlet portion 5 a to the outlet portion 5 b of the first areas. If forexample, the section of the first flow zone FZ1 first increases, andthen once again decreases, there would be a stagnation zone of thesecond fluid at the increase of the section, which would involve analteration of the laminar flow of the second fluid.

With regard to the first end 8 a, 9 a of the first baffles 8, 9,identifying, in a plane orthogonal to the axis of symmetry x-x (axisentering into the sheet with reference to the enclosed figures) of apartially surrounded hole 3, an initial angle α0 between an initial axisS0 parallel to the crossing direction A-A and passing through the centeror a central point of the partially surrounded hole 3 and a first axisS1 that extends from the center or central point of the partiallysurrounded hole 3 to the inlet portion 8 a of a baffle or recess 8, 9,the initial angle α0 is between 45° and 135°, preferably between 80° and100°.

If desired, identifying, in a plane orthogonal to the axis of symmetryx-x (axis entering into the sheet with reference to the enclosedfigures) of a partially surrounded hole 3, a first angle α1 between afirst axis S1 that extends from the center or a central point of thepartially surrounded hole 3 to the first end 8 a, 9 a of a baffle orrecess 8, 9 and a second axis S2 that extends from the center of thepartially surrounded hole 3 to the point of such baffle or recess 8, 9defining the termination or end of the constant section, the first angleis between 45° and 135°, preferably between the value of the initialangle α0 and 100°.

In addition, if the section of the first flow zone FZ1 is constant andthen converging or constant, then converging and finally diverging,identifying, in a plane orthogonal to the axis of symmetry x-x of thepartially surrounded hole 3, a second angle α2 between a second axis S2that extends from the center of the partially surrounded hole 3 to thepoint of a baffle or recess 8, 9 defining the termination or end of theconstant section and a third axis S3 that extends from the center of thepartially surrounded hole 3 to the point of such baffle or recess 8, 9defining the termination or end of the converging section, the secondangle is between 45° and 180°, preferably between the value of thesecond angle α2 and 150°.

Alternatively, if the section of the first flow zone FZ1 is convergingfor the entire extension thereof or converging and then diverging (suchvariant is not illustrated in the figures), identifying, in theorthogonal plane, a second angle α2 between a second axis S2 thatextends from the center of the partially surrounded hole 3 to the pointof a baffle or recess 8, 9 defining the first end 8 a, 9 a of a baffleor recess 8, 9 and a third axis S3 that extends from the center of thepartially surrounded hole 3 to the point of such baffle or recess 8, 9defining the termination or end of the converging section, the secondangle is between 45° and 180°, preferably between 45° and 150°.

If the section is constant and then diverging, identifying, in a planeorthogonal to the axis of symmetry x-x of the partially surrounded hole3, a third angle α3 between a second axis S2 that extends from thecenter of the partially surrounded hole 3 to the point of a baffle orrecess 8, 9 defining the termination or end of the constant section anda fourth axis S4 that extends from the center of the partiallysurrounded hole 3 to the point of such baffle or recess 8, 9 definingthe termination of the diverging section, the third angle α3 is between45° and 180°, preferably between the value of the first angle α1 and165°.

If instead the section is converging and then diverging or constant,then converging and finally diverging, identifying, in a planeorthogonal to the axis of symmetry x-x of the partially surrounded hole3, a third angle α3 between a third axis S3 that extends from the centerof the partially surrounded hole 3 to the point of a baffle or recess 8,9 defining the termination of the converging section and a fourth axisS4 that extends from the center of the partially surrounded hole 3 tothe point of such baffle or recess 8, 9 defining the termination of thediverging section, the third angle α3 is between 45° and 180°,preferably between the value of the second angle α2 and 165°.

Advantageously, the first baffles 8, 9 or the recesses can also beextended beyond a respective hole, i.e. they have terminal sectionscloser to the outlet portion 5 b relative to a respective hole and hencedefine a second flow zone FZ2, that actually constitutes a continuationof the first flow zone FZ1, and such second flow zone FZ2 is delimitedbetween terminal sections of the first baffles 8, 9 or recesses. Thesecond flow zone FZ2 is not extended around the respective partiallysurrounded hole 3.

In such a manner, one obtains a confinement of the second fluiddownstream of the partially surrounded hole 3, with the expressionconfinement “downstream” indicating a confinement of the second fluid inthe area or zone of the fin 1 that such fluid crosses after having hitthe hole 3 or better yet the tube 4 inserted in the hole 3.

The second flow zone FZ2 has a feeding mouth corresponding to thedelivery mouth of the first flow zone FZ1 as well as a mouth fordischarging the second fluid towards successive holes or parts of thefin with reference to the crossing direction A-A. The second flow zoneFZ2 or better yet the walls thereof are fluid-sealed so as to preventleaks or outflows of fluid between the delivery mouth and the dischargemouth.

The second flow zone FZ2 has a section that is divergent, evaluated withreference to a plane orthogonal to the plate and passing through thecenter of the hole 3 partially surrounded by the respective baffle 8, 9or groove.

With regard instead to the extrados 8 d, 9 d of the baffles 8, 9 orrecesses, i.e. the section of the baffles or recesses directed away fromthe respective partially surrounded hole 3, this is substantiallyrectilinear or slightly curved and does not have stagnation zones forthe second fluid. The concavity/convexity of the extrados 8 d, 9 ddepends on the velocity field that is established due to the presence ofother tubes.

More particularly, the extrados 8 d, 9 d is substantially tilted withrespect to the crossing direction A-A by an angle between −45° and 45°,preferably between 0° and +20° or between −15° and 45°, with an initialend 8 a, 9 a proximal to the inlet portion 5 a and distal from theoutlet portion 5 b and a final end 8 b, 9 b distal from the inletportion 5 a and proximal to the outlet portion 5 b, the initial ends 8a, 9 a of the extradoses 8 d, 9 d of the baffles or recesses 8, 9 of apartially surrounded hole 3 being at a distance from each other greaterthan the distance between the final ends 8 b, 9 b of the extradoses 8 d,9 d of such baffles or recesses 8, 9.

Preferably, the baffles 8, 9 or recesses have a configuration, withreference to the travel sense or crossing direction A-A of the secondfluid, with a first section 8 e with preferably constant width, a secondsection 8 f with preferably increasing width and then a third section 8g with preferably decreasing width. The second section 8 f has initialwidth equal to the first section 8 e and final width equal to 2-5 timesthe first section, preferably 3-4 times the first section 8 e.

Advantageously, the holes 3 are each extended around a respective axisof symmetry x-x, with the axes of symmetry x-x of the holes 3 beingsubstantially parallel to each other, while the first baffles 8, 9 orthe housing recesses for second baffles of a confinement unit 8, 9 aresubstantially symmetric to each other with respect to a plane passingthrough the crossing direction A-A from an inlet portion 5 a to anoutlet portion 5 b of the edge 5 and (passing) through the axis ofsymmetry x-x of the at least partially surrounded respective hole 3.

In addition, the delimiting wall 7 can have a collar section 7 cprojecting upward with respect to one of the main faces 6, while thefirst baffles 8, 9 of the partially surrounded hole 3 with collarsection 7 c are extended around at least one part of the collar section7 c distal from the inlet portion 5 a and facing towards the outletportion 5 b, the first or second baffles having height or thicknessequal to or greater than the collar section 7 c. The collar section 7 cof the delimiting walls 7 also carries out, in addition to the functionof heat transfer between fin and tube, also the function of spacerbetween two adjacent and successive fins 1 of a finned pack.

Advantageously, the first baffles 8, 9 or the recesses of one or moreconfinement units 8, 9 have a first end 8 a, 9 a proximal to the inletportion 5 a as well as a second end 8 b, 9 b distal from the inletportion 5 a of the plate 2. The first proximal 8 a, 9 a of the firstbaffles 8, 9 or housing recesses are at a first distance D1 from eachother, while the distal ends 8 b, 9 b of the first baffles 8, 9 orrecesses of a confinement unit are at a second distance D2 from eachother which is advantageously smaller than the first distance D1, suchthat the first baffles or recesses together delimit a first area that issubstantially tapered moving away from the inlet portion 5 a. Inaddition, in such case, preferably there are no intermediate sections ofthe first baffles 8, 9 with distance from each other greater than thefirst distance D1 between the first ends 8 a, 9 a.

If desired, the distance between the first baffles 8 could initiallydecrease moving away from the inlet portion 5 a and then, having reacheda minimum value at an intermediate portion of the first baffles, wherethe distance D3 between the baffles 8, 9 or recesses is minimal, onceagain increase up to the second end 8 b, 9 b; according to such variant,the distance D2 between the first baffles at the respective second end 8b, 9 b could also be greater than the distance D1. In such case, thearea between the proximal ends and the intermediate portions of thefirst baffles or of the housing recesses is substantially tapered in thesense moving away from the inlet portion 5 a, while a second area wouldbe provided between the intermediate portions and the second ends of thefirst baffles or of the housing recesses with an initial section withdecreasing cross section and then a terminal section with cross sectionincreasing moving away from the inlet portion 5 a.

More particularly, the distance between the baffles 8, 9 or recesses inthe sense moving away from the inlet portion 5 a can initiallyprogressively decrease and then, once a minimum value at an intermediateportion of the baffles or recesses has been reached, progressivelyincrease once again up to the second end 8 b, 9 b.

In addition, the (first and/or second) baffles can have a tubular bodyor solid block body, which at the intrados 8 h, 9 h, i.e. the section ofthe baffles 8, 9 or recesses directed towards or facing the respectivepartially surrounded hole 3, is substantially flat or slightly curvedwith trim, preferably, orthogonal or projecting upward with respect tothe plate 2. In addition, the (first and/or second) baffles are,preferably, fluid-sealed (if desired they are not perforated) so as toprevent the passage of the second fluid therethrough. In addition, eachbaffle is preferably formed in a single piece.

In substance, the intrados 8 h, 9 h of the baffles 8, 9 or of the secondbaffles is substantially continuous, so as to ensure the passage fromone section of the first flow zone FZ1 to another (from constant toconverging, from converging to diverging or from constant to diverging)in a gradual and progressive manner, i.e. there are no sudden passagesor steps from one section of such first flow zone to another or alongthe extension of each of the same.

More particularly, the intrados 8 h, 9 h along the first flow zone FZ1comprises a curved or substantially curved surface, better yet slightlycurved with concavity directed towards the first flow zone FZ1 itself atthe areas with constant section and/or converging section thereof, and acurved or substantially curved surface, better yet slightly curved withconcavity directed away from the flow zone itself at possible areas withdiverging section thereof.

If a second flow zone FZ2 is also provided, the intrados 8 h, 9 h of thebaffles 8, 9 or of the second baffles is made in a manner such that thepassage from a terminal section of the first flow zone FZ1 to the secondflow zone FZ2 occurs in a gradual and progressive manner, i.e. there areno sudden passages or steps between such zones. More particularly, theintrados 8 h, 9 h at the passage from the first FZ1 to the second FZ2flow zone comprises a curved surface or better yet slightly curvedsurface with concavity directed towards the extrados 8 d, 9 d.

The intrados 8 h, 9 h is therefore not flat or rectilinear.

If desired, the first baffles comprise a first drawn or cut and bentportion 2 a of the plate 2, i.e. the baffles 8, 9 are obtained by meansof drawing of the plate 2 itself. If a collar section 7 c is provided,then both the first baffles 8, 9 and the collar sections 7 c areobtained by means of drawing a respective plate 2.

The at least one drawn portion 2 a of the plate 2 can be tapered movingaway from the main extension plane of the plate 2, such that such drawnportion has a tip or free end 2 a 1 of lower width with respect to thebase or end thereof for constraining 2 a 2 to the plate.

Each drawn portion 2 a preferably has two separate and drawn sections 2a 3, 2 a 4 defining a channel or opening 11 therebetween, e.g.substantially tapered, the ends of which together defining the tip 2 a 1and the base 2 a 2 of the drawn portion 2 a. As will be understood, forthe obtainment of such drawn portion 2 a the drawing of a portion ofplate 2 will be carried out followed by the removal of the endsubstantially parallel to the plate 2 by means of cutting or incision,in such a manner obtaining the two separate sections 2 a 3, 2 a 4. Theseparate sections 2 a 3, 2 a 4 preferably have thickness lower than theremaining part of the plate 2, since the drawing determines or candetermine a “stretching” of the edges, so as to increase the exposedsurface area thereof and reduce their thickness.

In such case, the plate 2 can have second drawn portions, each set todefine a collar section 7 c, which in this case could be tapered likethe first drawn portions. Such second drawn portions ensure a goodtransfer of the heat between fin and tubes.

Alternatively, the (first and/or second) baffles 8, 9 can comprise atubular body or solid block body with trim substantially orthogonal tothe plate 2, and such tubular body or solid block body can be formedapart or separately with respect to the plate 2 and connected, ifdesired via welding or fitting with the plate 2. In addition, secondbaffles could be formed apart and inserted each in a respective recessfor housing a confinement unit 8, 9, and such baffles could have aconfiguration and, during use, arrangement substantially correspondingto the baffles 8, 9.

For such purpose, the second baffles could be metal sections obtainedvia extrusion, molding or shaping and mechanically inserted in the finsof a finned pack or better yet in the plates thereof, for example withforced insertion or via interference or by means of use of weldingmaterials or alloys that facilitate the adhesion and the transmission ofthe heat. Clearly, the second baffles entirely fill the respectiverecesses, such that after the insertion of the second baffles there areno remaining parts of the recesses still open or not filled.

The height or thickness of the (first and/or second) baffles 8, 9, oreven the pitch of the fins or distance between two successive fins,could vary from about 0.1 mm to about 36 mm.

In addition, in order to define the position of the baffles, one or moreholes 3 will be considered with substantially circular or evennon-circular cross section, e.g. oval, elliptical, etcetera and thefirst portion 7 a and the second portion 7 b with cross section that issubstantially semi-circular, semi-oval, semi-elliptical, etcetera.

In addition, each baffle 8, 9 or recess can be at a third distance D4from the delimiting wall 7 and more particularly from a section of thesecond portion 7 b of the delimiting wall 7 between about 0.05R andabout 3R, where with R the radius of a tube 3 or of a partiallysurrounded hole is indicated.

A fin like that illustrated in FIGS. 1 to 4 allows reducing theso-called “dead zone” downstream of the tubes, with reference to thedirection A-A of the flow of the second fluid.

The baffles 8, 9 or in any case the baffles insertable in the housingrecesses in fact determine, as can be verified, a conveyance orconfinement of the second fluid on the second portion 7 b of therespective delimiting wall 7 and hence towards the respective tube 4,which ensures that each portion of the delimiting wall 7 and hence ofthe respective tube is hit by the second fluid.

A fin according to the present invention preferably comprises one, twoor more rows of holes 3, offset or aligned with respect to each otherwith respect to the crossing direction A-A, such that each row of holes3 is at a distance from the inlet portion 5 a that is different withrespect to the other rows of holes 3.

As indicated above, a baffle 8, 9 according to the present invention canhave tubular configuration defining an opening or first opening 11 (seeFIGS. 5 and 6), if desired extended substantially parallel to the axisof symmetry x-x of the respective hole 3.

Such opening 11 is typically used for the passage through the respectivebaffle, i.e. in a direction substantially parallel to the axis x-x, of athird fluid F3 such to increase the exchange efficiency of theexchanger. In addition, the opening 11 could also be fed with the firstF1 or the second F2 fluid.

It should then be noted that also the baffles 8, 9 described above couldhave an opening or channel 11, such to have a structure that issubstantially tubular with through opening extended substantiallyparallel to the axis of symmetry x-x of the respective hole 3.

The first opening 11 of one or more baffles could have a section withany suitable shape, e.g. circular, elliptical, rectangular or polygonal.

In addition, in each baffle, two or more openings or micro-channels 11could also be provided. Regarding such aspect, one or more baffles couldalso delimit two or more channels or openings for the conveyance of twodifferent fluids or for sending a same fluid between one channel and thenext.

Clearly, an opening 11 as indicated above can be present in particularif the baffles comprise metal sections obtained—via extrusion, moldingor shaping—apart with respect to the plates 2 and then mechanicallyinserted in the plates 2 themselves, or portions 2 a obtained viadrawing or shaping of the plate 2 a.

In addition, the first opening 11 is delimited at the second 8 f andthird section 8 g or at the first 8 e, second 8 f and third 8 g section.

If desired, the baffles 8, 9 comprise a tubular body with thickness thatis substantially constant, such that the delimiting wall for the opening11 has constant thickness.

With reference now in particular to the geometry and distribution of theholes in a fin according to the present invention, the following will bedefined:

-   -   line or row of holes 3 or of tubes 4 is the set of the holes of        a fin or of the tubes inserted therein at a same distance from        the inlet portion 5 a;    -   A or PT is the pitch or distance of the holes 3 or of the tubes        4 of a same row of tubes times the number of tubes of such row;        and    -   B or PR is the pitch or distance of the lines times the number        of lines.

On the basis of such definitions, a fin according to the presentinvention could have A×B between 10 mm×10 mm and 200 mm×200 mm.

In the following table, several possible geometries and sizes arereported for a fin according to the present invention as well as for thetubes to be inserted in the same.

In addition, there could also be a fin with A×B equal to 48×41.75 or50×40 with tubes of diameter equal to 12 mm or 16 mm, or A×B equal to20×20 with tubes with 5 mm diameter.

With regard instead to the definition “offset” of the tubes or of theholes, it is intended that the holes of adjacent and successive rows areoffset with reference to the crossing direction A-A, while thedefinition “square” indicates that the holes or the tubes of adjacentand successive rows are aligned, still with reference to the crossingdirection A-A. For such purpose, in a fin according to the presentinvention, each row of holes 3 comprises at least one hole aligned alongthe crossing direction A-A with a respective hole of the other rows ofholes and/or at least one hole offset with respect to the holes 3 of theother rows of holes 3, still with reference to the crossing directionA-A.

In substance, a fin according to the present invention comprises two ormore lines or rows of holes 3, i.e. groups of holes substantially at asame distance from the inlet portion 5 a. In addition, the holes ofadjacent and successive rows can be offset or aligned with reference tothe crossing direction A-A.

In addition, in a fin according to the present invention, there may ormay not be holes for the positioning of heating elements, e.g. throughholes with diameter equal to 9.5 mm.

The thickness of a fin according to the present invention can varybetween 0.1 mm and 2 mm.

The distance D5 of the intrados 8 h, 9 h of a baffle 8, 9 or recess atthe first end 8 a, 9 a of the baffles or recesses from the initial axisS0 parallel to the crossing direction A-A, and passing through thecenter or a central point of the partially surrounded hole 3, can thusbe as indicated hereinbelow:

(R1+0.1 mm)sin(α0)<D5<PT/2

wherein R1 is the radius of a partially surrounded hole 3.

Preferably, D5 is greater than 1.2R1 and smaller than 2.2R1.

The distance D6 of the extrados 8 d, 9 d of a baffle 8, 9 or recess atthe first end 8 a, 9 a of the baffles or recesses from the initial axisS0 parallel to the crossing direction A-A, and passing through thecenter or a central point of the partially surrounded hole 3, can thusbe as indicated hereinbelow:

(R1+0.1 mm)sin(α0)<D6<PT/2

wherein R1 is the radius of a partially surrounded hole 3.

Preferably, D6 is greater than D5 and smaller than D5+2 mm.

With regard to D2, this can thus be as indicated hereinbelow:

D3/2<D2/2<PT/2

Preferably, D2/2 is greater than D3/2 and smaller than D6.

The length D8 of the extrados 8 d, 9 d of the baffles or recesses can beas indicated hereinbelow:

R1<D8<PR

Preferably, D8 is greater than 0.8PR and smaller than 1.2PR.

In addition, if the first flow zone FZ1 has a section, evaluated withreference to a plane orthogonal to the plate 2 and passing through thecenter or a central point of the respective partially surrounded hole 3,constant and then converging, or constant, then converging and finallydiverging, or always constant or always converging, then, havingconsidered D9 to be the value of the distance of the partiallysurrounded hole 3 from a baffle 8, 9 or recess at the termination of theconstant section and, if provided, the start of the converging section,and D10 to be the value of the distance of the partially surrounded holefrom a baffle 8, 9 or recess at the termination of the convergingsection, D9 and D10 can be as indicated hereinbelow:

0.1 mm<D9<PT/2−R1

0.1 mm<D10<D9

Preferably, D9 is greater than 0.9(D5/sin(α0)−R1) and smaller thanD5/sin(α0)−R1, while D10 is greater than 0.6(D5/sin(α0)−R1) and smallerthan 0.9(D5/sin(α0)−R1).

With regard to D3, this can be as indicated hereinbelow:

(R1+D10+0.1 mm)sin(α3)<D3/2<PT/2

Preferably, D3/2 is greater than 0.4(D5/sin(α0)−R1) and smaller thanD5/sin(α0)−R1.

The pitch or distance between the fins can vary between 1.2 and 36 mm.

With regard instead to FZ2, this is a zone with a section which variesbetween completely constant and completely diverging, with constant anddivergent sections alternating with each other and dependent on themutual position of the tubes 4 and on their shape. The length of thezone FZ2 is extended from 0 up to a line distance of 0.2 mm, withtypical range of 0 to ¾ the line distance. The region between twobaffles of two rows of tubes defines a further channel that has asection which can be a combination of straight, converging and divergingsections so as to guide the flow (there could be a line offset with thetube that is in the middle). Each section will have a length comprisedbetween 0 and the overall length of the baffle.

A fin 1 according to the present invention can then have a smoothsurface or so-called “w_vaffle”, “pyramid” or “turbulence” surface. Suchfin can also have an edge so-called “cap-like” or “smooth”.

The fin 1 could be made of any suitable material, e.g. aluminum,aluminum alloys, copper, copper alloys, steel, stainless steel made ofdifferent alloys, such as AISI 304, AISI 316, etcetera.

In addition, the fin 1 could be finished with surface treatments, e.g.painting, cataphoresis or other treatments.

With reference now to FIG. 7, a finned pack 10 is illustrated accordingto the present invention for heat exchangers, which comprises aplurality of fins 1 according to the present invention, placed insuccession one after the other or one alongside the other andsubstantially parallel to each other. Each fin 1 also has its throughholes 3 aligned with the through holes 3 of the other fins 1.

The finned pack 10 then comprises an opening 10 a for introducing asecond fluid between pairs of fins of the plurality of fins, and anoutlet opening 10 b for the second fluid between the pairs of fins. Thefins 1 have the inlet portions 5 a thereof at the introduction opening10 a and the outlet portions 5 b thereof at the outlet opening 10 b.

In the exchanger, provision is also made for a plurality of tubes 4inserted in the aligned through holes of the plurality of fins 1, thetubes 4 having a first sector 4 a directed towards the inlet opening 10a as well as a second sector 4 b directed towards the outlet opening 10b, the fins 1 having the confinement unit(s) 8, 9 around a portion of asecond sector of a respective tube 4.

If the finned pack 10 is provided with two or more adjacent andsuccessive fins with drawn portions 2 a, then the tip 2 a 1 of the drawnportions 2 a of a plate of one of such fins 1 is fit in the base 2 a 2or better yet in the opening defined by the base 2 a 2 of the drawnportions 2 a of an adjacent and successive fin 2.

As already stated above, the facing main faces 6 of two adjacent andsuccessive fins 1 together delimit a respective area of passage orcrossing of a second fluid that hits respective sections of tubes 4inserted in such fins, and such tubes 4 as well as the baffles areextended through the passage areas so as to be hit by the flow of thesecond fluid.

The finned pack 10 can then comprise an upper tile 10 c, a lower tile 10d and in addition at one side, manifolds 10 f for the tubes 4, and onthe other side forks 10 g for transmitting the first fluid between twotubes 4.

If desired, each fin has at least one confinement unit with two throughrecesses for positioning baffles and each through recess of eachconfinement unit is aligned with a respective recess of the other fins.In such case, the finned pack 10 also comprises two baffles for eachconfinement unit, each inserted in a respective series of alignedthrough recesses of the fins 1, preferably of all the fins of the finnedpack 10.

According to such variant, the baffles or bars could constitute amechanical load-bearing element of the finned pack 10.

In addition, if the baffles delimit an opening 11, the finned pack 10 orbetter yet the respective heat exchanger could comprise means forfeeding a third fluid or the first fluid into the opening 11 of one ormore baffles 8, 9. In such case, at the end of the baffles 8, 9, outletscould be provided, along with tubular connection elements between theend of a baffle and a respective end of another baffle. In substance, insuch case a circuit can be provided for feeding a third fluidconstituted by the baffles connected with each other in series and/or inparallel. Alternatively, the baffles could be connected in series and/orin parallel with each other and with the tubes 4, such that baffles andtubes would be fed with the first fluid.

Alternatively, the opening 11 could be simply placed in communicationwith the outside without providing for feeding the first or a thirdfluid within the same.

The tubes 4 of a finned pack 10 could be made, for example, of copperand its alloys, stainless steel and its alloys, iron and its alloys,aluminum and its alloys or other suitable materials.

The tubes could also have an internal wall that is smooth, grooved, e.g.tilted grooved, helical grooved or grooved with cross spirals.

The tubes could then have a diameter between 4 and 90 mm, advantageouslybetween 5 and 22 mm, preferably 5 mm, 6.35 mm, 7.2 mm, 7.9 mm, 9.5 mm,12 mm, 14, 16 mm or 22 mm.

The thickness of the tubes instead preferably varies between 0.15 and 3mm, and, still more preferably, is equal to 0.25 mm, 0.28 mm, 0.32 mm,0.35 mm, 0.4 mm or 0.5 mm.

A finned pack according to the present invention can be integrated orinstalled in:

-   -   a condenser, fluid cooler (dry cooler), gas cooler 13 (see FIGS.        8-9), i.e. a machine intended for the heat exchange between a        fluid to be condensed (if two-phase) or cooled and the        environment, which can employ liquid, aeriform or gaseous        coolant fluids;    -   an evaporator or air cooler, i.e. a machine intended for the        heat exchange between a coolant fluid being evaporated/heated        and a secondary fluid (air) to be cooled, which can employ        liquid, two-phase or gaseous coolant fluids;

As will be understood, a fin and a finned pack according to the presentinvention allow conveying the second fluid around the entire surface ofthe holes and hence of the tubes of the fin, also in the zone of eachtube that is directed towards the outlet portion.

Indeed, for such purpose, it has been verified that with fins and finnedpacks according to the state of the art, the second fluid correctly anduniformly hits and affects the part of the tubes directed towards theinlet portion of the fins, but in the zone between the tubes of one rowand the tubes of a successive row, the second fluid “detaches” from theexternal surface of the tubes, hence it does not affect the part of thetubes directed towards the outlet portion of the fins. Naturally, thisinvolves a considerable reduction of the heat exchange efficiency sincemost of the external face of the tubes crossed by the first fluid is notin heat exchange contact with the second fluid.

Due to the confinement units of a fin according to the present inventionand of a respective finned pack, the second fluid is instead actuallyguided and maintained close to the tubes even in the zone downstreamthereof, so as to affect and place the second fluid in heat exchangewith the entire external face of the tubes and the portion of the fin 2downstream of the tube 3, considerably improving the obtainable heatexchange efficiency.

In order to demonstrate the capacities and advantages obtainable bymeans of a fin according to the present invention, hereinbelow the heatconduction in general and then through the same fin will be analyzed.

As can be understood, in order to facilitate the cooling and the heatingof the fin surfaces, baffles have been proposed that are intended to belicked by a fluid current (e.g. air), which are provided with the sameobject of increasing the thermally active surface and, hence, reducingthe overall thermal resistance of the fin.

Such solution addresses a thermo-fluid-dynamic problem that has twoaspects:

-   -   conduction through the baffles;    -   convection between the surface of the baffles and the fluid or        second fluid.

First, with regard to the conduction through the baffles, the base ofthe baffles, in particular when the same are obtained by means ofdrawing of a plate, is in direct contact with a surface (the plate 2) athigh temperature, T_(w), while the lateral skirt thereof is hit with afluid current (second fluid) that is cooler, which maintains the surfaceof the skirt of the baffles at a temperature T_(m)(x) lower than that ofthe hot body (main body of the plate 2) and variable as a function ofthe distance x from the body itself. This temperature difference causesa conductive heat flow, qx(cond), through the base of the baffles:

$q_{x{({cond})}} = {{- k}\; \frac{\delta \; T}{\delta \; x}}$

which assumes the form

$q_{x{({cond})}} = {{- k}\; \frac{\delta \; \theta}{\delta \; x}}$

wherein θ=T(x)−T_(α) is the temperature difference between baffle andfluid.

The energy that, in this manner, enters within the baffles is removedvia convection through the lateral skirt and the terminal surfacethereof. The convective heat flow can be evaluated with the followingexpression:

{umlaut over (q)} _(x) =hA(T(x)−T _(α))

From the comparison of the above-reported expressions, it will beunderstood that the problem of the conductive flow is of greaterinterest, so that the problem desired to be resolved is that of findinga geometry that optimizes this heat exchange.

Having considered the geometric complexity of baffles or recesses for afin according to the present invention, for a more thorough and completedescription, three zones are identified that are indicated FZ0, FZ1 andFZ2, in which FZ0 is the initial flow zone around a tube 4 before orupstream of the inlet portion 8 a, 9 a or of the first flow zone FZ1.

With reference to the zone FZ0, the part relative to the problem of theseparation of the limit layer will be discussed; such problem ismanifested at about the maximum radius (diameter) of the cylinder ortube 4 hit by the flow. As widely documented in fluid mechanics, when atube is hit with a flow, a flow dead zone is determined that ischaracterized by a region of stationary recirculation, which is formeddownstream of the tube itself, thus allowing the complete separation ofthe dynamic flow at the geometric region affected by thevortical-stationary recirculation.

With reference to the two tubes 4 of a fin illustrated in FIG. 2,indicating as the first “Tube 1” that on the right in the figure and“Tube 2” that on the left in the figure, the flow of the second fluidafter having hit tube 1 is once again stabilized after having exceededthe domain due to the stationary recirculation, by linking with thefront part 4 a of a successive cylinder or tube placed in another lineor successive line (Tube 2). Hence, the dead zone downstream of tube 1licked by the stationary recirculation unequivocally deteriorates theconvective heat transfer between the second fluid and the first fluidthat crosses tube 1.

With reference to the second flow zone FZ2, the geometric role performedby the thermo-fluid-dynamic flow baffles (in passive or active mode,i.e. without or with opening 11) will instead be described as a newsolution for reducing the stationary recirculation (dead zone) so as toincrease the transfer of convective heat.

Finally, with reference to the first flow zone FZ1, the assembly of thethree zones will be described as well as the thermo-fluid-dynamicsolutions brought thereby.

The increase of the heat convection essentially regards the study of theheat exchange between a solid surface and a fluid that is moving withrespect thereto.

For such purpose, considering the tube 1 on the right in FIG. 2 as atwo-dimensional cylindrical geometric surface correlated with a pair offluid-dynamic baffles 8, 9, the characteristics and the function of suchbaffles determine the working mode of the fin and hence of a respectiveexchanger.

As a consequence of the particular geometry of the baffles, part of theflow that licks the tube 4 and the baffles 8, 9 will be obliged to bechanneled along the “trajectory/conduit” generated or definedtherebetween.

Due to the viscosity of the second fluid, the more the second fluidchanneled into the trajectory/conduit approaches the wall of the tube 4or of the baffles 8, 9, the more the fluid-wall relative speed decreases(but the total speed does not decrease, rather this is increased), untilit is nearly canceled at the wall interface, where a sudden structuralchange is geometrically generated in the system of fluid-dynamic bafflessuch to determine an increase of the useful heat exchange section, withcorresponding and consequent decrease of the speed and increase of thepressure of the second fluid.

In light of the latter consideration, it is clear that between the wallsdefined by the particular geometry (trajectory/conduit), there is aclear increase of the heat conduction, due to the increase of the heatexchange surface areas (baffles) and, if desired, also due to theincrease of speed if the section is converging (with consequent decreaseof pressure that can therefore be rebalanced as a function of the loadloss caused by the conduit converging downstream of the divergingsection of the tube/baffles system) generated by the walls of thetube/baffles conduit, which determines a separation of the fluid threadmuch further downstream of the tube, thus considerably decreasing thevortex of stationary recirculation downstream of the tube itself.

This therefore translates into a further increase of the useful heatexchange between the geometric structures (tube/baffles). The outletsection of the baffles is designed so as to determine a realignment anddirectional linking of the exiting flow with the tube of the successiveline, in such a manner exploiting the increase of pressure generated inthe section with possible divergence.

It should also be underlined that the temperature gradient that appearsin the equation q=A{umlaut over (q)}=hAΔT(1′), proportional to thequantity of heat removed from or transferred by the fluid, depends onthe macroscopic motion of the fluid itself. For this reason, it is clearin this geometric case that it is necessary to use the equations offluid-dynamics together with the principle of energy conservation indescribing the phenomenon of convection.

In addition, the type of fluid motion has such an effect on the heatexchange that it is possible to obtain various convection types. Inparticular, in the present description, the presence of forcedconvection will be considered.

In the modality of convective exchange between tube 4 and baffles 8, 9in passive mode (i.e. without hole or opening 11 in the baffles), therelation commonly employed for expressing the heat flow is indicated in(1′), in which the specific heat flow {umlaut over (q)} is proportionalto a suitable temperature difference ΔT between flow and wall(naturally, both in the passive case—lack of openings 11 in the bafflessystem—and in the active case—presence of openings 11 in the baffles—thetemperature difference ΔT considerably changes as a function not only ofthe presence/absence of the openings 11 in the baffles, but also as afunction of the geometry thereof, also taking under consideration thefact that the baffles do not necessarily have internal/externalsymmetry, i.e. between the internal part or intrados, e.g.converging/diverging, and the external part or extrados, e.g. linearpart of the baffles).

The equation (1′) is known as Newton's Law and the proportionalityconstant h[W/(m²K)] is termed coefficient of convective heat exchangeor, more simply, convective coefficient. It is considered that h, unlikethe heat conductivity, is not a thermo-physical property of the fluid,but it should be considered as an “easy” operating definition, useful inevaluating the quantity of heat exchanged in a convective manner.

Another dimensionless ratio of considerable importance in thedescription of the particular geometry of baffles in passive mode,employed for convective heat exchange, is the Nusselt number, Nu, whichrepresents the ratio between the convective heat flow and the conductiveheat flow in the fluid. In order to determine the mathematic expression,a fluid layer is considered with thickness L and moving with respect toa solid wall.

Given the considerable complexity of the calculation for describing thephenomena affected by the particular geometry, work will be mainlyconducted in ideal and symmetry mode only in the geometric part wheresuch symmetry exists between tube and baffles, and passive mode (absenceof openings in the baffles). The presence of the opening 11 in thebaffles considerably complicates the calculation, given the possibilityto generate not only different temperature gradients between the wallsof the tube conduit/baffles, but also different densities before andafter the constancy/convergence/divergence system, with the consequencethat for a correct development of the calculation, average quantitiesmust be used as a function of the geometry of the considered system.

In this situation, only the geometric part of the system in passive modewill be analyzed, hence with baffles without openings 11.

Hence, we assume that the second fluid placed at distance L from thesolid surface (tube conduit/baffles), at temperature T_(p), is attemperature T_(∞). As already seen above, the heat flow can be expressedby means of the equation q=A{umlaut over (q)}=hAΔT as:

q _(conv) =h′(T _(p) −T _(∞))  (2′)

If the fluid layer was (macroscopically) immobile, there would also beconduction and the specific conductive heat flow could be expressed, bymeans of Fourier's law, as:

${\overset{¨}{q}({cond})} = {\frac{k}{L}\left( {T_{p} - T_{\infty}} \right)\left( 3^{\prime} \right)}$

From the definition of Nusselt number

${Nu}\overset{\Delta}{=}{\frac{q_{\overset{¨}{conv}}}{q_{\overset{¨}{cond}}} = {\frac{h\; L}{k}\left( 4^{\prime} \right)}}$

Therefore, a high value of the Nusselt number, Nu, indicates a highefficiency of the convective process of heat exchange with respect tothe merely conductive heat exchange of the fluid. As already stated, thefluid adheres to the wall and, then, in proximity thereto there is alsoconduction. For this reason, the specific convective heat flow can alsobe expressed, by means of Fourier's law, as:

$q_{conv} = {{{- K}\frac{\delta \; T}{\delta \; y}¨\mspace{14mu} {per}\mspace{14mu} y} = {0\left( 5^{\prime} \right)}}$

Combining the equations (4′) and (5′), one obtains:

${Nu} = {\frac{h\; L}{k} = {{\frac{- \left( \frac{\delta \; T}{\delta \; y} \right)}{\Delta \; T}\mspace{14mu} {per}\mspace{14mu} y} = {0\left( 6^{\prime} \right)}}}$

from which it is inferred that the coefficient of convective heatexchange, h, depends on the temperature gradient of the wall fluid (inour case, the coefficient of heat exchange depends not only on thepreviously claimed conditions, but also on the nature of the structuralmaterial of the device used for the heat exchange).

As previously stated, the forced convection used in the tube/bafflessystem subjected to technical/analytical description assumes theexistence of a fluid in relative motion with respect to a solid surface.As a function of the geometry of the latter, it is possible to make adistinction within the forced convection. Indeed, it is possible todistinguish between:

-   -   forced convection of the external motion;    -   forced convection of the internal motion, within ducts.

In the present case, there is a partial mixture of both convections, andfurther calculation difficulties arise therefrom.

Such classification is important since the different parameterscharacterizing the system (e.g. the Reynolds number, Re) assumedifferent expressions in the two cases.

In the external outflows (i.e. those which pass outside the baffles orthe extradoses thereof), for example, the motion of the fluid occurs inan unlimited region (or one that approaches this), around or inproximity to a solid surface. Usually, in this case, it is assumed thatthe speed μ_(∞), and the temperature T_(∞), of the fluid in theundisturbed region are known. The temperature difference that appears inthe expression q=A{umlaut over (q)}=hAΔT must this case be assumed asequal to:

ΔT=T _(p) −T _(∞)  (1)

while the Reynolds number, Re, is defined as:

$\begin{matrix}{{Re}\overset{\Delta}{=}{{Re}_{x} = \frac{u_{\infty}}{v}}} & (2)\end{matrix}$

With regard to the internal outflows (e.g. within a duct or within theregion that comprises the first FZ1 and the second FZ2 flow zone), thetemperature difference of the equation (1′) is assumed equal to:

ΔT−T _(p) −T _(b)  (3)

Where T_(b) is the so-called bulk temperature or average temperature.The latter is also termed mixing cup temperature, since it is thetemperature which would be obtained by placing the entire fluid in anadiabatic container and mixing so as to eliminate any thermal gradient.This is very important in the internal outflows since there is noanalogous undisturbed temperature T_(∞).

The bulk temperature in a given section of the duct is defined as inequation 5:

$\begin{matrix}{T_{b}\overset{\Delta}{=}\frac{\int_{A_{s}}{{puc}_{y}{TdA}_{s}}}{\overset{.}{m}c_{x}}} & (5)\end{matrix}$

If it is set that the fluid is incompressible, (in the case of air, thefluid is to compressible, but we can use the assumption ofincompressibility given the operating conditions involved) and thephysical properties are known and constant, equation 5 becomes:

$\begin{matrix}{T_{b}\overset{\Delta}{=}\frac{\int_{A_{s}}{uTdA}_{s}}{\overset{.}{V}}} & (6)\end{matrix}$

In the case of constant heat flow, after a first zone, termed of heatdevelopment, the difference between wall temperature and averagetemperature is maintained constant. However, in the case of constantwall temperature, the average temperature tends asymptotically to becomethat of the wall.

Regarding the Reynolds number, Re, this is defined:

$\begin{matrix}{{Re}\overset{\Delta}{=}{{Re}_{D} = \frac{u_{m}D_{h}}{v}}} & (7)\end{matrix}$

wherein

u_(m) is the average speed of the fluid,

ν is the kinematic viscosity of the fluid, and

D_(h) is the hydraulic diameter defined as:

$\begin{matrix}{D_{h}\overset{\Delta}{=}\frac{4A}{P}} & (8)\end{matrix}$

wherein with A it is intended the area of the section of the duct withwet perimeter P. Other aspects that distinguish the two types of forcedconvection are the formation and development of the speed and thermallimit layers.

First of all, one considers an external outflow such as that of a fluidon a flat surface. The distance δx from the flat wall in orthogonaldirection y is termed thickness of the limit layer and is defined asthat value for which there is:

u _(y)=0.99u _(∞)  (9)

where

u_(y) is the speed of the fluid at distance y from the wall whichincreases with the increase of x.

u∞ is the speed of the undisturbed fluid

The quantity δt is termed thickness of the thermal limit layer and isdefined as that value of y for which one has:

$\begin{matrix}{\frac{T_{p} - T_{(y)}}{T_{p} - T_{\infty}} = 0.99} & (10)\end{matrix}$

If the wall temperature T_(p) is constant and independent from x, thethickness of the thermal limit layer increases with the increase of x.As a consequence, the temperature gradient along y progressivelydecreases in moving away from the leading edge of a plate or sheet.Therefore, the coefficient of convective heat exchange h, and hence theheat flow {umlaut over (q)}, decrease with the increase of x. In thecase of internal outflows, the presence of the border surfacesconditions both the formation and the shape of the speed and thermallimit layers, and in this motion type it is possible to identify tworegions: that of the inlet, where the motion is not developed, and thatwhere the motion is completely developed. It is necessary at this pointto better specify what is intended by completely developed motion.

Considering the inlet speed profile to be uniform, as soon as the fluidenters into a channel, the particles closest to the wall delimiting suchchannel undergo, due to the viscosity of the fluid, a deceleration whilethe particles at the center of the channel, in order to maintain theflow rate constant, are accelerated. In such a manner, two limit layersare formed which tend to be thickened along the direction of the motionand that, if the distance L between the plates defining the channel isnot high with respect to the length of the channel, are joined togetherat a certain distance x_(v) from the inlet edge. After this point, aparabolic speed distribution is created, typical of the fully developedlaminar profile of Couette motion, which no longer varies with theincrease of the distance on the inlet edge.

The distance x_(v) is termed length of dynamic development ortheoretical initial length, and it can be evaluated with differentempirical formulas, such as the following

$\begin{matrix}{\frac{x_{v}}{D} = {0.0575{Re}}} & (11)\end{matrix}$

due to Langhaar:

valid for ducts of circular section with diameter D and for Reynoldsnumbers less than 2300.

With regard to the heat field, the entering fluid is at the uniformtemperature T while the walls can be considered at the uniform andconstant temperature T_(p) and subject to a constant heat flow {umlautover (q)}.

In such case, as the fluid proceeds along a duct, a thermal limit layeris formed, in proximity to both interfaces, which is identical to thatof the isolated profile. Nevertheless, continuing in the sense of themotion, these two tend to be thickened until they are joined at adistance x_(t), from the inlet edge, which is termed thermal developmentlength, and finally defined as that distance from the inlet for whichthe Nusselt number differs by 5% from the value corresponding to thedeveloped thermal operating conditions.

In laminar operating conditions, the value of x_(t) depends on thethermal conditions at the wall and can be evaluated with the empiricalexpression 12, in the case of assigned wall temperatures, and 13, in thecase of imposed heat flow.

$\begin{matrix}{\frac{x_{t}}{D_{h}} = {0.033{Re}_{D_{h}}\Pr}} & (12) \\{\frac{x_{t}}{D_{h}} = {0.045{Re}_{D_{h}}\Pr}} & (13)\end{matrix}$

The Prandtl number,

${\Pr = {\frac{v}{\alpha} = \frac{c_{p}\mu}{k}}},$

can assume values that are extremely different from each other based onthe type of fluid selected. This dimensionless group is given by theratio between the molecular properties of transport of the quantity ofmotion and heat and can be interpreted as the ratio between the thermallimit layer and the thermal viscous layer. If the Prandtl number, aswith air, is close to one, then the two development lengths are of thesame order of magnitude. If however it is much lower than one, thelength of fluid-dynamic development is much greater than the thermallength. Indeed, in this case the transmission of heat is so efficientthat the problem may sometimes be treated as a merely conductive one(case of liquid metals).

Finally, if the Prandlt number is much greater than one, or theviscosity of the fluid is very high, the fluid-dynamic limit layer ismuch thicker than the thermal limit layer.

From that stated above, it is observed that the temperature, unlike thespeed, continues to vary with the increase of the distance from theinlet edge of the baffle. This would lead to the assumption that it isimpossible to attain condition of complete development. Nevertheless, ifone considers the dimensionless ratio (which can be considered adimensionless temperature):

$\begin{matrix}\frac{T_{p} - T}{T_{p} - T_{b}} & (14)\end{matrix}$

it can be demonstrated that, in suitable conditions, this becomesindependent from x. It can be verified that, even if the temperature Tvaries along the duct, the shape of its profile in the channel remainsconstant. In these conditions, then, one can speak of complete thermaldevelopment, and there is:

$\begin{matrix}{{\frac{\delta}{\delta \; x}\left\lbrack \frac{T_{p} - T}{T_{p} - T_{b}} \right\rbrack} = 0} & (15)\end{matrix}$

Since, according to equation 15, the ratio between the temperaturedifferences is independent of x, the same must hold true for itsderivative with respect to y. In addition, by evaluating the aforesaidderivative in proximity to the wall and recalling that T_(p) and T_(b)are by definition independent from y, one obtains:

$\begin{matrix}{{\frac{\delta}{\delta \; x}\left\lbrack \frac{T_{p} - T}{T_{p} - T_{b}} \right\rbrack} = {{\frac{\frac{{- \delta}\; T}{\delta \; y}}{T_{s} - T_{b}} \neq {{f(x)}\mspace{14mu} {per}\mspace{14mu} y}} = 0}} & (16)\end{matrix}$

from Fourier's law, one obtains

$\begin{matrix}{{q_{p} = {{- K}\frac{{- \delta}\; T}{\delta \; y}}},{{{per}\mspace{14mu} y} = 0}} & (17)\end{matrix}$

while from Newton's law

q _(p) ={umlaut over (h)}(T _(p) −T _(b))  (18)

Combining the equations, one obtains

$\begin{matrix}{\frac{h}{k} \neq {f(x)}} & (19)\end{matrix}$

Therefore, in the internal outflows, in conditions of complete thermaldevelopment, for a fluid with constant physical properties, the localconvective coefficient is constant and independent. Given that theNusselt number, Nu, is strictly tied to the convective coefficient, thelength of thermal development can also be defined as that distance fromthe inlet edge for which the Nusselt number differs by 5% from the valuecorresponding to the developed thermal operating conditions.

Therefore, a solution with passive baffles, hence without openings 11(see FIG. 2) determines:

-   -   a reduction of the dead zone (region in which the fluid does not        wet the tube), with consequent increase of the heat exchange        efficiency; given the same number of tubes, there can be an        increase up to a theoretical maximum of the exchange surface        area of about 50%;    -   an optimization of the flows within the exchanger and improved        exploitation of the fluid flow, since the second fluid is        channeled and conveyed on the walls of the tube, minimizing the        paths that do not have heat exchange;    -   an increase of the exchange surface areas if there is a        fin/baffle thermal contact, with consequent increase of the        exchange and hence of the efficiency;    -   an increase of the efficiency since there is an increase of the        convective exchange in the duct or flow zones created by the        baffle.

The increase of performances is obtained with a marginal increase of theexpenses necessary for the creation of the baffles, which can beobtained by means of fitting of the surfaces directly drawn from thesurface of the existing fin.

In the case of baffles with drawn portions, the increase of the exchangesurface area is in any case ensured and the geometry of the duct (andhence the shape of the baffle) can be reproduced with high accuracy.

The improved situation with the technical solution of FIG. 2 can befurther optimized by employing an active strategy with regard to thebaffles, i.e. by providing for baffles with openings 11.

In the case of baffles without openings, the baffles behave as passiveelements, since their temperature is determined by the situation ofequilibrium that is created between the heat transferred from the finand that exchanged with the fluid. In such case, the baffles 8, 9 havethe double function of increasing the exchange on the main tube 4 andincreasing the total surface area of heat exchange of the fin.

The calculations are possible in the case of passive baffles, since theboundary conditions for the heat transmission differential equation aresimple (uniform temperature given by the conduction through thebaffles).

An increase of efficiency of the system can be obtained if the bafflesare no longer employed only for deflecting the flow and increasing theexchange surface area, but also for increasing the forced exchange ofheat. According to the solution of FIG. 5, two further channels oropenings 11 are created, for which there can be the following possibleuse solutions:

a) no fluid within the channels, i.e. the first fluid; in such case, itis possible to exploit, in the case of natural convection, the stackeffect created within the channels in order to have a passive exchange,in any case surely more efficient than the exchange given by just thefins;

b) fluid within the channels 11 equal to the fluid within the tubes 4,with temperature equivalent or different;

c) fluid within the channels 11 different from that within the tubes 4,with temperature equivalent or different between such fluids.

The proposed system has various applications.

An application of type c) with fluid in the channels 11 different fromthat of the tubes 4 is obtained in the applications of cooling thesecond fluid by means of a first fluid moving within the tubes 4. Insuch case, in particular when the temperature of the second fluid fallsbelow 0° C., there is the formation of frost or ice around the tube 4and on the fins 2. In order to remove such formation of frost or ice, soto prevent reducing the heat exchange, various systems are usedincluding the presence of rod-like electrical heating elements suitablyinserted between the tubes 4 in suitable holes created in the fins 2, orby means percolation systems for percolating water at suitabletemperature, higher than 0° C., from the upper part of the exchanger, orby means of cycle inversion, in the case of the evaporators, by makinghot gas condense within the tubes 4 or by passing water suitably mixedwith compounds adapted to lower the cryoscopic point of the mixtureitself within the tubes 4. Within baffles 8-9, a fluid at suitabletemperature can then be passed that can operate the defrosting of thetubes 4 and fin 2 in a localized manner, with the advantage of:

-   -   operating defrosting in a dedicated circuit without having to        modify the circuit of the first fluid within the tube 4;    -   increasing the efficiency of the defrosting, given that the        defrosting circuit is potentially localized in proximity to all        the tubes 4;    -   having the possibility of regulating the defrosting power as a        function of the zone to be defrosted (i.e. where there is a        greater formation of frost or ice).

If the fluid within the channels 11 is different from that in the tubes,consequences are not obtained from the operating or functionalstandpoint with respect to the case in which the fluid is the same,unless the temperature in the tubes 4 and in the channels 11 isdifferent. Hereinbelow, the temperature difference between the fluid inthe tubes and that in the channels will be considered, allconsiderations remaining valid whatever the fluid used.

In case a), the calculations exactly follow the same line traced for thesystem with baffles of passive type, since the boundary conditions arethe same.

In such case, there is the possibility of a second heat exchange withinthe channels 11 (in free convection) which could lead to an increase ofefficiency of the system due to the stack effect, that could naturallylead to a further fraction of heat outside the exchanger. The Nusseltnumber is no longer a function of the Reynolds number since the airpresent within the channels 11 has zero or in any case negligible speed,while the floating forces are those which start to play a fundamentalrole.

In cases b) and c), the complication in the calculation of the heatexchange is provided by the boundary conditions which in this caseprovide for the internal surface of the baffle at a new constanttemperature T_(d) with respect to the rest of the exchanger. Once again,there is a conductive exchange between tube 4 and baffles 8, 9 and thereis a forced convective exchange between tube 4 and second fluid, but inthis case the temperature is no longer constant within the channel 11and uniform at the edges. A temperature gradient is established in theduct between the walls of the tube+fin and that of the baffle atdifferent temperature. There is an asymmetry of the temperature fieldand, consequently, of those of density and speed. The two cases b) andc) provide different (and symmetric) solutions in accordance with thesign of the temperature difference between channels 11 and tube 4. Thesimplification proposed for the passive case can be employed herein ifthe temperature differences are small.

We assume, as a first case, that the temperature of the fluid within thechannels 11, and consequently T_(d), is lower than that of the wall ofthe tube T_(p). In such case, the conductive heat flow will lead to anelimination of the heat from the tube 4 towards the

$\begin{matrix}{q_{x{({cond})}} = {{- k}\frac{\delta \; T}{\delta \; x}}} & \;\end{matrix}$

baffle, which increases with the increase of temperature gradient thatone is able to establish. The system will function as a double-flowexchanger in which the transfer of heat between the two fluids (in thetube 4 and in the channels 11) occurs via pure conduction. Together withthis conduction, however, we also have the convective part within theflow zones created by the baffles. The calculation complication is givenby the boundary conditions which depend on the conduction equation. Thethermal gradient that is established leads to having a complextemperature field, determined by the two wall temperatures, by theirthermal connection and by the temperature of the fluid which passesinside the channels.

In order to compare the problem of the exchange, we have the possibilityto execute some approximations. We can reasonably assume that due to thetemperature gradient, the fluid carries out two independent heatexchanges with the two surfaces (in realty, there is a further exchangewith the fin, which we can consider similar to that of the passive caseor that without the baffles). Indeed, in laminar operating conditions,the duct can be divided into two semi-ducts in which the (undisturbed)temperature end point is not reached at the center line, but at adistance from the walls proportional to the temperature differencebetween wall and fluid. The point will be situated closer to the colderwall than from the warmer wall. In a first approximation, we cantherefore consider the two exchanges independent, treating them with theformalism proposed for the passive baffle. The movement of the thermalwell from the center line towards the colder wall uses a greaterquantity of fluid for the heat exchange, thus increasing the machineoutput.

The system can then be employed for any type of exchanger. Inparticular, each tube of an existing geometry can be substituted withthe tube+baffles assembly. From the structural standpoint, the systemcan be easily made by means of cutting and drawing the existing fin soas to create a continuous and load-bearing system of channels for thestructure.

Therefore, a solution with active baffles, hence with openings 11 (seeFIGS. 5 and 6) determines:

-   -   a reduction of the dead zone, with consequent increase of the        heat exchange efficiency, this being obtained due to the        presence of the baffles 8, 9, independent of the auxiliary        function thereof;    -   an increase of the efficiency since there is an increase of the        convective exchange in the duct 11 created by the baffles 8, 9;    -   an optimization of the flows within the exchanger and improved        exploitation of the fluid flow, since the fluid is channeled and        conveyed on the walls of the tube and the paths which do not        have heat exchange are minimized;    -   a more effective transfer of heat from the tube 4 towards the        fluids which circulate in the system (in the flow zones and        within the baffles), in particular when the temperature of the        fluid in the baffle is lower than that of the tube;    -   an increase of the output due to the greater surface areas of        heat exchange, if the temperature in the tubes 4 and in the        baffles 8, 9 is the same, for example if the same circuit        supplies both the tubes 4 and the channels 11; and    -   an increase of the performances, even if there is the structural        requirement to construct a secondary circuit.

Modifications and variations of the invention are possible within theprotective scope defined by the claims.

1. A fin for a finned pack for heat exchangers, comprising a plate inwhich a plurality of through holes is obtained for the positioning oftubes intended to convey a first heat exchange fluid, said plate havingan edge as well as two main faces each intended to be licked by a secondheat exchange fluid in a crossing direction (A-A) from an inlet portionto an outlet portion of said edge of said plate, said holes beingdelimited by a respective inner delimiting wall of said plate includinga first portion facing towards said inlet portion and a second portionfacing towards said outlet portion, said fin comprising at least oneconfinement unit of said second fluid arranged around a hole of saidplurality of holes so as to obtain at least one partially surroundedhole, said at least one confinement unit comprising two baffles or twothrough recesses for housing baffles arranged one opposite the otherwith respect to a respective partially surrounded hole as well as eachsurrounding and spaced from a respective section of said second portionof said delimiting wall of said partially surrounded hole, so as toconfine, during use, on said plate a first flow zone (FZ1) of saidsecond fluid between each baffle or recess and a respective section ofsaid second portion of said delimiting wall, wherein said first flowzone (FZ1) has section, evaluated with reference to a plane orthogonalto said plate and passing through the center or central point of therespective partially surrounded hole, that is constant for the entireextension thereof, constant and then diverging, converging for theentire extension thereof, converging and then diverging, constant andthen converging, or constant, then converging and finally diverging, andwherein the intrados of said baffles or said recesses along said firstflow zone (FZ1), i.e. the section of said baffles or recesses facingtowards or facing the respective partially surrounded hole, comprises acurved or substantially curved surface with concavity facing towardssaid first flow zone (FZ1) at the areas with constant and/or convergingsection of said first flow zone (FZ1), and a curved or substantiallycurved surface with concavity facing away from said first flow zone(FZ1) itself at the optional areas with diverging section of said firstflow zone (FZ1).
 2. The fin according to claim 1, wherein said firstflow zone (FZ1) does not have first areas with section, evaluated withreference to a plane orthogonal to said plate and passing through thecenter of the respective partially surrounded hole, greater than areasdownstream and upstream of said first areas.
 3. The fin according toclaim 1, wherein by identifying, in a plane orthogonal to the symmetryaxis x-x of a partially surrounded hole, an initial angle between aninitial axis (S0) parallel to said crossing direction (A-A) and passingthrough the center or a central point of the partially surrounded holeand a first axis (S1) which extends from the center or central point ofthe partially surrounded hole to the inlet portion of a baffle orrecess, said initial angle is between 45° and 135°, preferably between80° and 100°.
 4. The fin according to claim 3, wherein by identifying,in a plane orthogonal to the symmetry axis (x-x) of a partiallysurrounded hole, a first angle between a first axis (S1) which extendsfrom the center or a central point of the partially surrounded hole tothe first end of a baffle or recess and a second axis (S2) which extendsfrom the center of the partially surrounded hole to the point of suchbaffle or recess defining the termination or end of said sectionconstant, the first angle is between 45° and 135°.
 5. The fin accordingto claim 4, wherein said first angle has a value between the value ofthe initial angle and 100°.
 6. The fin according to claim 1, wherein ifsaid section of said first flow zone (FZ1) is constant and thenconverging or constant, then converging and finally diverging, byidentifying in a plane orthogonal to the symmetry axis (x-x) of thepartially surrounded hole a second angle between a second axis (S2)which extends from the center of the partially surrounded hole to thepoint of a baffle or recess defining the termination or the end of theconstant section and a third axis (S3) which extends from the center ofthe partially surrounded hole to the point of such baffle or recessdefining the termination or the end of the converging section, saidsecond angle is between 45° and 180°, whereas if the section of saidfirst flow zone (FZ1) is converging for the entire extension thereof orconverging and then diverging, by identifying in the plane orthogonal asecond angle between a second axis (S2) which extends from the center ofthe partially surrounded hole to the point of a baffle or recessdefining the first end of a baffle or recess and a third axis (S3) whichextends from the center of the partially surrounded hole to the point ofsuch baffle or recess defining the termination or the end of theconverging section, the second angle is between 45° and 180°, preferablybetween 45° and 150°.
 7. The fin according to claim 4, wherein saidsection is constant and then converging or constant, then converging andfinally diverging, and wherein said second angle has a value comprisedbetween the value of said first angle and 150°.
 8. The fin according toclaim 4, wherein if said section is constant and then diverging, byidentifying in a plane orthogonal to the symmetry axis (x-x) of thepartially surrounded hole a third angle between a second axis (S2) whichextends from the center of the partially surrounded hole to the point ofa baffle or recess defining the termination or the end of the sectionconstant and a fourth axis (S4) which extends from the center of thepartially surrounded hole to the point of such baffle or recess definingthe termination of the diverging section, the third angle is between 45°and 180°, whereas if the section is converging and then diverging orconstant, then converging and finally diverging, by identifying in aplane orthogonal to the symmetry axis (x-x) of the partially surroundedhole a third angle between a third axis (S3) which extends from thecenter of the partially surrounded hole to the point of a baffle orrecess defining the termination of the converging section and a fourthaxis (S4) which extends from the center of the partially surrounded holeto the point of such baffle or recess defining the termination of thediverging section, the third angle is between 45° and 180°.
 9. The finaccording to claim 4, wherein said section is constant and thendiverging, wherein said third angle has a value comprised between thevalue of said first angle and 165°.
 10. The fin according to claim 1,wherein said baffles or said housing recesses are extended beyond arespective partially surrounded hole, i.e. said baffles or said housingrecesses have terminal sections closer to said outlet portion withrespect to a respective partially surrounded hole and defining a secondflow zone (FZ2) constituting a continuation of said first flow zone(FZ1), said second flow zone (FZ2) not extending around said partiallysurrounded hole, said second flow zone (FZ2) having a supply mouthcorresponding to the dispensing mouth of said first flow zone (FZ1) aswell as a discharge mouth for said second fluid towards parts of saidfin subsequent in the direction of said crossing direction (A-A), saidsecond flow zone (FZ1) having a section, evaluated with reference to aplane orthogonal to said plate and passing through the center of therespective partially surrounded hole, that is diverging.
 11. The finaccording to claim 1, wherein the baffles or the housing recesses of arespective confinement unit have a first end proximal to said inletportion, a second end distal from said inlet portion of said plate andwherein the distance between said baffles or said recesses in thedirection moving away from the inlet portion initially progressivelydecreases and then, once a minimal value has been reached at anintermediate portion of said baffles or recesses, progressivelyincreases once again up to said second end.
 12. The fin according toclaim 1, wherein extrados of said baffles or said recesses, i.e. thesection of said baffles or said recesses facing away from the respectivepartially surrounded hole, is substantially rectilinear or slightlycurved and does not have depression or stagnation zones for said secondfluid.
 13. The fin according to claim 12, wherein said extrados issubstantially tilted with respect to said crossing direction (A-A) foran angle between −45° and 45°, with an initial end proximal to saidinlet portion and distal from said outlet portion and a final end distalfrom said inlet portion and proximal to said outlet portion, the initialends of the extrados of the baffles or recesses of a partiallysurrounded hole being situated at a distance from each other greaterthan the distance between the final ends of the extradoses of suchbaffles or recesses.
 14. The fin according to claim 12, wherein eachbaffle or recess of said at least one confinement unit has intrados thatis not parallel to the respective extrados, i.e. the section of thebaffles or recesses facing away from the respective partially surroundedhole.
 15. The fin according to claim 1, wherein said baffles or recesseshave a configuration, with reference to the travel direction of saidsecond fluid on said plate, with a first section with constant width, asecond section with increasing width and then a third section withdecreasing width.
 16. The fin according to claim 1, wherein said baffleshave a substantially tubular structure so as to delimit at least onefirst opening or channel.
 17. The fin according to claim 16, whereinsaid at least one first opening or channel is substantially extendedparallel to the symmetry axis (x-x) of the respective hole and is set toallow the passage through the respective baffle and in a directionsubstantially parallel to said symmetry axis (x-x) of a third fluid orof said first fluid or is set to be arranged in communication with theoutside.
 18. The fin according to claim 15, wherein said first openingis delimited at said second and said third section or at said first,said second and said third section.
 19. The fin according to claim 16,wherein said baffles comprise a tubular body with substantially constantthickness.
 20. The fin according to claim 1, wherein said bafflescomprise at least one drawn portion of the plate, i.e. said baffles areobtained by means of drawing of said plate.
 21. The fin according toclaim 20, wherein said at least drawn portion of said plate is taperedmoving away from the main extension plane of said plate, such that saidat least one drawn portion has a free end or tip with lower width thanits base or end for constraining to the plate.
 22. A finned pack for aheat exchanger, comprising: a plurality of fins according to claim 1arranged in succession one after the other and substantially parallel toeach other, each fin having its through holes aligned with the throughholes of the other fins; a introduction opening for introducing a secondfluid between pairs of fins of said plurality of fins, said fins havingtheir inlet portions at said introduction opening; an outlet opening forsaid second fluid between said pairs of fins, said fins having theiroutlet portions at said outlet opening; a plurality of tubes fitted inthe aligned through holes of said plurality of fins, said tubes having afirst sector facing towards said inlet opening as well as a secondsector facing towards said outlet opening; and said fins having aconfinement unit around a portion of a second sector of at least one ofsaid tubes.
 23. The finned pack according to claim 22, wherein said tipof the drawn portions of a plate is fitted in the base or better yet inthe opening defined by the base of the drawn portions of an adjacent andsuccessive fin.
 24. A heat exchanger with finned pack comprising atleast one finned pack according to claim
 22. 25. The fin according toclaim 8, wherein said section is converging and then diverging orconstant, then converging and finally diverging, and wherein said thirdangle has a value comprised between the value of said second angle and165°.